This document proposes a new 5-axis NURBS curve interpolator that can be used with various 5-axis machining centers. It presents the processing sequence which involves CAD, CAM, and CNC systems. A new G-code format is introduced that is independent of machine rotational axes. An experiment shows the proposed interpolator has superior performance over conventional linear interpolation in terms of higher feedrates, lower contour errors, and tool orientation errors.

1. REAL TIME 5-AXIS NURBS CURVE INTERPOLATOR
Sungchul Jee and Taehoon Koo
 Processing Sequence
 CAD
 Comparing with Linear interpolation
 Example
 A CL file necessarily includes coordinates and tool orientation
vector in local coordinates.
▪ The proposed 5-axis NURBS interpolation format can be applied to various configuration
of 5-axis machining centers without modifying the NC code.
▪ The results of simulation and experiment validate the superiority of the proposed NURBS
interpolator over the conventional linear interpolator.
 6 control points and duplicated knots at start and end points
Geometry information
NURBS-IGES format
 CAM
5-axis NURBS G-code
 CNC
CL file format
Interpreter (ISO-6983)
5-axis NURBS interpolator
Parser
CATIA format: x_, y_, z_, i_, j_, k_
Ex) GOTO / -35.014, -65.185, 102.102, -0.416, -0.110, 0.902
HyperMill format: x[/_] y[/_] z[/_] u[/_] v[/_] w[/_]
Ex) 31:oL[10](x[/10.0] y[/31.2] z[/21.3] u[/0] v[/-0.557] w[/0.830]
Vector converter
TCP control
Added a new parser rule and
a vector conversion rule
Coordinate data and
tool orientation vectors
 The vector converter decomposes the tool orientation into two
angles for rotational axes depending on machine configuration.
 Interpolated data is transformed to joint axial movement by
TCP(Tool Center Point) control
Objective: ▪ To propose a new 5-axis NURBS interpolator that can be easily cope with
post-processing of CL files from a CAM system
▪ To evaluate and compare with the conventional linear interpolator
Rational B-spline curve entity (Type 126)
Ex) 126,5,3,1,0,1,0,0.,0.,0.,0.,0.333333,0.666667,1.,1.,1.,1.,1.,1., 7P 4
1.,1.,1.,1.,-178.,109.,0.,-166.,128.,0.,-144.,109.,0.,-109., 7P 5
Machine configuration
parameters
Sample code
G106 F0.9
X-43 Y-43 Z0
X-30.787 Y-34.290 Z9
X-18.574 Y-25.581 Z9
X-6.361 Y-16.872 Z-9
X5.850 Y-8.163 Z-9
X18.063 Y0.545 Z0
I-0.569 J-0.406 K0.7
I-0.429 J-0.429 K0.7
I-0.347 J-0.370 K0.7
I-0.381 J-0.149 K0.7
I-0.299 J-0.090 K0.7
I-0.158 J-0.113 K0.7
R0 R0 R0 R0.25 R0.5 R0.75
R1 R1 R1
TTTR
A
C
 New G-code Format
 The proposed G-code
 Independent of machine tool’s rotational axes
Format Description
G106 P_ ;
X_ Y_ Z_
I_ J_ K_
R_ W_;
…
G106: Start NURBS interpolation
P: Degree of a NURBS curve
X, Y, Z: Control point
I, J, K: Tool axis vector
R: Knot
W: Weight (default value = 1)
 Experiment
Mechatrolink II
protocol
<Servo System>
Yaskawa S-II
<Control PC>
Simultaneous 5-Axis
Control system
NT110 digital
commnunication
board
Digital motion network system
PCI slot type
S-II
0 20 40 60 80
0
5
10
15
20
25
Feedrate[mm/s]
5-Axis NURBS Interpolation
Linear Interpolation
Length of Curve [mm]
0 20 40 60 80
0
1
2
3
4
5
Length of Curve [mm]
Contourerror[mmx10
-3
]
5-Axis NURBS interpolation
Linear interppolation
0 20 40 60 80
0.000
0.004
0.008
0.012
0.016
ToolOrientationError[deg.]
5-Axis NURBS Interpolation
Linear Interpolation
Length of Curve [mm]
 Max. allowable chord error for linear interpolation : 1μm
 Feedrate : 0.9m/m
Feedrate
Contour error
Tool orientation error